If \(\log_{10}y + 3\log_{10}x \geq \log_{10}x\), express y in terms of x.
- A. \(y \geq \frac{1}{x}\)
- B. \(y \leq \frac{1}{x}\)
- C. \(y \leq \frac{1}{x^{2}}\)
- D. \(y \geq \frac{1}{x^{2}}\)
Solve for x in the equation \(5^{x} \times 5^{x + 1} = 25\).
- A. \(-2\)
- B. \(\frac{-1}{2}\)
- C. \(\frac{1}{2}\)
- D. \(2\)
If (2t – 3s)(t – s) = 0, find \(\frac{t}{s}\).
- A. \(\frac{3}{2}\) or \(1\)
- B. \(\frac{3}{2}\) or \(-1\)
- C. \(\frac{-3}{2}\) or \(-1\)
- D. \(\frac{-3}{2}\) or \(1\)
The remainder when \(x^{3} – 2x + m\) is divided by \(x – 1\) is equal to the remainder when \(2x^{3} + x – m\) is divided by \(2x + 1\). Find the value of m.
- A. \(\frac{-7}{8}\)
- B. \(\frac{-3}{8}\)
- C. \(\frac{1}{8}\)
- D. \(\frac{5}{8}\)
If the solution set of \(x^{2} + kx – 5 = 0\) is (-1, 5), find the value of k.
- A. -6
- B. -4
- C. 4
- D. 5
Factorize completely: \(x^{2} + x^{2}y + 3x – 10y + 3xy – 10\).
- A. (x + 2)(x + 5)(y + 1)
- B. (x + 2)(x - 5)(y + 1)
- C. (x - 2)(x + 5)(y + 1)
- D. (x - 2)(x - 5)(y + 1)
If \(y = 4x – 1\), list the range of the domain \({-2 \leq x \leq 2}\), where x is an integer.
- A. {-9, -1, 2,3, 4}
- B. {-9, -2, 0, 1, 7}
- C. {-5, -4, -3, -2}
- D. {-9, -5, -1, 3, 7}
If \(f(x) = \frac{4}{x} – 1, x \neq 0\), find \(f^{-1}(7)\).
- A. \(\frac{-3}{7}\)
- B. \(0\)
- C. \(\frac{1}{2}\)
- D. \(4\)
Consider the statements:
p : Musa is short
q : Musa is brilliant
Which of the following represents the statement “Musa is short but not brilliant”?
- A. \(p \vee q\)
- B. \(p \vee \sim q\)
- C. \(p \wedge \sim q\)
- D. \(p \wedge q\)
An operation * is defined on the set, R, of real numbers by \(p * q = p + q + 2pq\). If the identity element is 0, find the value of p for which the operation has no inverse.
- A. \(\frac{-1}{2}\)
- B. \(0\)
- C. \(\frac{2}{3}\)
- D. \(2\)
Express \(\frac{8 – 3\sqrt{6}}{2\sqrt{3} + 3\sqrt{2}}\) in the form \(p\sqrt{3} + q\sqrt{2}\).
- A. \(7\sqrt{3} - \frac{17\sqrt{2}}{3}\)
- B. \(7\sqrt{2} - \frac{17\sqrt{3}}{3}\)
- C. \(-7\sqrt{2} + \frac{17\sqrt{3}}{3}\)
- D. \(-7\sqrt{3} - \frac{17\sqrt{2}}{3}\)
If \(P = {x : -2 < x < 5}\) and \(Q = {x : -5 < x < 2}\) are subsets of \(\mu = {x : -5 \leq x \leq 5}\), where x is a real number, find \((P \cup Q)\).
- A. \({x : -5 < x < 5}\)
- B. \({x : -5 \leq x \leq 5}\)
- C. \({x : -5 \leq x < 5}\)
- D. \({x : -5 < x \leq 5}\)
Two functions f and g are defined on the set of real numbers by \(f : x \to x^{2} + 1\) and \(g : x \to x – 2\). Find f o g.
- A. \(x^{2} + 4x - 5\)
- B. \(x^{2} - 4x + 5\)
- C. \(x^{2} - 1\)
- D. \(x - 1\)
A car is moving at 120\(kmh^{-1}\). Find its speed in \(ms^{-1}\).
- A. 33.3\(ms^{-1}\)
- B. 66.6\(ms^{-1}\)
- C. 99.9\(ms^{-1}\)
- D. 120.0\(ms^{-1}\)
A particle starts from rest and moves through a distance \(S = 12t^{2} – 2t^{3}\) metres in time t seconds. Find its acceleration in 1 second.
- A. 24\(ms^{-2}\)
- B. 18\(ms^{-2}\)
- C. 12\(ms^{-2}\)
- D. 10\(ms^{-2}\)
Find the constant term in the binomial expansion \((2x^{2} + \frac{1}{x})^{9}\)
- A. 84
- B. 168
- C. 336
- D. 672
Find the angle between forces of magnitude 7N and 4N if their resultant has a magnitude of 9N.
- A. 39.45°
- B. 73.40°
- C. 75.34°
- D. 106.60°
A body of mass 28g, initially at rest is acted upon by a force, F Newtons. If it attains a velocity of \(5.4ms^{-1}\) in 18 seconds, find the value of F.
- A. 0.0082N
- B. 0.0084N
- C. 0.082N
- D. 0.084N
If \(\overrightarrow{OX} = \begin{pmatrix} -7 \\ 6 \end{pmatrix}\) and \(\overrightarrow{OY} = \begin{pmatrix} 16 \\ -11 \end{pmatrix}\), find \(\overrightarrow{YX}\).
- A. \(\begin{pmatrix} 9 \\ -5 \end{pmatrix}\)
- B. \(\begin{pmatrix} -23 \\ -5 \end{pmatrix}\)
- C. \(\begin{pmatrix} 9 \\ 17 \end{pmatrix}\)
- D. \(\begin{pmatrix} -23 \\ 17 \end{pmatrix}\)
What is the probability of obtaining a head and a six when a fair coin and and a die are tossed together?
- A. \(\frac{1}{12}\)
- B. \(\frac{1}{3}\)
- C. \(\frac{1}{2}\)
- D. \(\frac{2}{3}\)